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nordsb [41]
2 years ago
8

Use right triangle tools to find the unknown measures. Round lengths to the nearest tenth and angle measures to the nearest degr

ee.

Mathematics
1 answer:
timama [110]2 years ago
5 0

Step-by-step explanation:

OP=11.2

m<Q= 42⁰

m<R=48⁰

The tools used are....

I have used the property of Pythagoras Theorm to get the length of side QP, I have also used the property of inverse function of sin to get the measure of angle Q and the property of sum of angles of triangle to get measure of angle of R

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Trace several round objects onto the grid on Math Masters, page 436

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3 years ago
Expand (2 + a)9 using Pascal’s triangle.
Natalija [7]

Answer:

Step-by-step explanation:

The Pascal triangle is used to determine the coefficients of the terms when we expand the expression.

                                             1                                (A + B) ^ 0 = 1

                                         1       1                            (A +B ) ^ 1 = 1A + 1B

                                   1          2        1          (A+ B) ^ 2 = 1A^2 + 2 AB + 1B^2

By extending the triangle, you will get the 9th row, which is your expression, of the coefficients. that is

1          9       36    84    126    126    84    36    9    1

Now, fill in AB in the gaps.

1AB + 9 AB + 36AB + 84AB + 126AB + 126AB +84AB + 36AB + 9AB + 1AB

Next, you need to go from the left to fill out the exponent of A and it will go down from 9 (the exponent of the whole thing) . That is

1A^9B+9A^8B+36A^7B+84A^6B+126A^5B+126A^4B+84A^3B+36A^2B+9A^1B+1A^0B

Next will be the exponent of B. this time, you go from the right and do the same with A. You can go from the left also, but go up from 0 to 9 for the exponent of B

1A^9B^0+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+1A^0B^9

The last step is just to simplify the A^0=1 and B^0 =1 at the first and the last terms.

A^9+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+B^9

Hope you can learn the method

5 0
2 years ago
Write the equation of the trigonometric graph.
prisoha [69]

Answer:

f(x)= \sin(6x)+3

Step-by-step explanation:

The parent function of this graph is:  y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

f(x) = \sf A \sin (B(x + C)) + D

  • A = amplitude (height from the mid-line to the peak)
  • 2π/B = period (horizontal distance between consecutive peaks)
  • C = phase shift (horizontal shift - positive is to the left)
  • D = vertical shift

The parent function y = sin(x) has the following:

  • Amplitude (A) = 1
  • Period = 2π
  • Phase shift (C) = 0
  • Vertical shift (D) = 0
  • Mid-line:  y = 0

From inspection of the given graph:

  • Amplitude (A) = 1
  • \sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}
  • Phase shift (C) = 0
  • Vertical shift (D) = +3  (as mid-line is y = 3)

\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6

Substituting the values into the standard form:

\implies f(x) =1 \sin (6(x + 0)) + 3

\implies f(x) = \sin (6x) + 3

Therefore, the equation of the given trigonometric graph is:

f(x)= \sin(6x)+3

6 0
1 year ago
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